Document Type : Original Article
Authors
1 Payame Noor University, Tehran, Iran.
2 K.N.Toosi University of Technology Tehran, Iran.
Abstract
This paper introduces a two stage stochastic programming to address strategic hub location decisions and tactical flight routes decisions for various customer classes considering uncertainty in demands. We considered the airline network with the arc capacitated single hub location problem based on complete–star p-hub network. In fact, the flight routes are allowed to stop at most two different hubs. The first stage of the model (strategic level) determines the network configuration, which does not change in a short space of time. The second stage is dedicated to specify a service network consists of determining the flight routes and providing booking limits for all itineraries and fare classes after realization of uncertain scenarios. To deal with the demands uncertainty, a stochastic variations caused by seasonally passengers’ demands through a number of scenarios is considered. Since airline transportation networks may face different disruptions in both airport hubs and communication links (for example due to the severe weather), proposed model controls the minimum reliability for the network structure. Due to the computational complexity of the resulted model, a hybrid algorithm improved by a caching technique based on genetic operators is provided to find a near optimal solution for the problem. Numerical experiments are carried out on the Turkish network data set. The performance of the solutions obtained by the proposed algorithm is compared with the pure GA and Particle Swarm Optimization (PSO) in terms of the computational time requirements and solution quality.
Keywords
Adibi, A. and Razmi, J., (2015). "2-Stage stochastic programming approach for hub location problem under uncertainty: A case study of air network of Iran", Journal of Air Transport Management, Vol. 47, pp. 172-178.
Alibeyg, A., Contreras, I. and Fernández, E., (2016). "Hub network design problems with profits", Transportation Research Part E: Logistics and Transportation Review, Vol. 96, pp. 40-59.
Alumur, S. and Kara, B.Y., (2008). "Network hub location problems: The state of the art", European journal of operational research, Vol.190, No. 1, pp. 1-21.
Alumur, S.A., Nickel, S. and Saldanha-da-Gama, F., (2012). "Hub location under uncertainty", Transportation Research Part B: Methodological, Vol. 46, No. 4, pp. 529-543.
An, Y., Zhang, Y. and Zeng, B., (2015). "The reliable hub-and-spoke design problem: Models and algorithms", Transportation Research Part B: Methodological, Vol. 77, pp. 103-122.
Aslani, S., Modarres, M. and Sibdari, S., (2014). "On the fairness of airlines’ ticket pricing as a result of revenue management techniques", Journal of Air Transport Management, Vol. 40, pp. 56-64.
Azizi, N., Chauhan, S., Salhi, S. and Vidyarthi, N., (2016). "The impact of hub failure in hub-and-spoke networks: Mathematical formulations and solution techniques", Computers & Operations Research, Vol. 65, pp. 174-188.
Belobaba, P.P. and Weatherford, L.R., (1996). "Comparing decision rules that incorporate customer diversion in perishable asset revenue management situations", Decision Sciences, Vol. 27, No. 2, pp. 343-363.
Belobaba, P.P., (1989). "OR practice—application of a probabilistic decision model to airline seat inventory control", Operations Research, Vol. 37, No. 2, pp. 183-197.
Birge, J. R., & Louveaux, F. (2011). Introduction to stochastic programming. Springer Science & Business Media.
Brumelle, S.L. and McGill, J.I., (1993). "Airline seat allocation with multiple nested fare classes", Operations research, Vol. 41, No. 1, pp. 127-137.
Campbell, J.F. and O'Kelly, M.E., (2012). "Twenty-five years of hub location research", Transportation Science, Vol. 46, No. 2, pp. 153-169.
Çetiner, D., (2013). Fair revenue sharing mechanisms for strategic passenger airline alliances (Vol. 668). Springer Science & Business Media.
Chen, S., Gallego, G., Li, M.Z. and Lin, B., (2010). "Optimal seat allocation for two-flight problems with a flexible demand segment", European Journal of Operational Research, Vol. 201, No. 3, pp. 897-908.
Cizaire, C. and Belobaba, P., (2013). "Joint optimization of airline pricing and fare class seat allocation", Journal of Revenue and Pricing Management, Vol. 12, No. 1, pp. 83-93.
Contreras, I., Cordeau, J.F. and Laporte, G., (2011). "Stochastic uncapacitated hub location", European Journal of Operational Research, Vol. 212, No. 3, pp. 518-528.
Čvokić, D.D. and Stanimirović, Z., (2020). A single allocation hub location and pricing problem. Computational and Applied Mathematics, Vol. 39, No. 1, pp.1-24.
Damgacioglu, H., Dinler, D., Ozdemirel, N.E. and Iyigun, C., (2015). "A genetic algorithm for the uncapacitated single allocation planar hub location problem", Computers & Operations Research, Vol. 62, pp. 224-236.
Davari, S., Zarandi, M.H.F. and Turksen, I.B., (2010), July. The fuzzy reliable hub location problem. In 2010 Annual Meeting of the North American Fuzzy Information Processing Society (pp. 1-6). IEEE.
Eghbali, M., Abedzadeh, M. and Setak, M., (2014). "Multi-objective reliable hub covering location considering customer convenience using NSGA-II", International Journal of System Assurance Engineering and Management, Vol. 5, No. 3, pp. 450-460.
Farahani, R.Z., Hekmatfar, M., Arabani, A.B. and Nikbakhsh, E., (2013). "Hub location problems: A review of models, classification, solution techniques, and applications", Computers & Industrial Engineering, Vol. 64, No. 4, pp. 1096-1109.
Holland, J. H. (1975). Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. U Michigan Press.
Hou, Y.T., Huo, J.Z. and Chu, F., (2019b). "An Integrated Problem of-Hub Location and Revenue Management with Multiple Capacity Levels under Disruptions", Journal of Advanced Transportation, 2019.
Huo, J.Z., Hou, Y.T., Chu, F. and He, J.K., (2019a). "A Combined Average-Case and Worst-Case Analysis for an Integrated Hub Location and Revenue Management Problem", Discrete Dynamics in Nature and Society.
Kara, B.Y. and Tansel, B.C., (2000). "On the single-assignment p-hub center problem", European Journal of Operational Research, Vol. 125, No. 43, pp. 648-655.
Kim, H. and O'Kelly, M.E., (2009). "Reliable p-hub location problems in telecommunication networks", Geographical Analysis, Vol. 41, No. 3, pp. 283-306.
Kratica, J., Stanimirović, Z., Tošić, D. and Filipović, V., (2007). "Two genetic algorithms for solving the uncapacitated single allocation p-hub median problem", European Journal of Operational Research, Vol. 182, No. 1, pp. 15-28.
Lapp, M. and Weatherford, L., (2014). "Airline network revenue management: Considerations for implementation", Journal of Revenue and Pricing Management, Vol. 13, No. 2, pp. 83-112.
Lin, C.C. and Lee, S.C., (2018). "Hub network design problem with profit optimization for time-definite LTL freight transportation", Transportation Research Part E: Logistics and Transportation Review, Vol. 114, pp. 104-120.
Littlewood, K., (1972). "Forecasting and control of passenger bookings", Airline Group International Federation of Operational Research Societies Proceedings, 1972, Vol. 12, pp. 95-117.
Lüer-Villagra, A. and Marianov, V., (2013). "A competitive hub location and pricing problem", European journal of operational research, Vol. 231, No. 3, pp. 734-744.
M.C. Ferris (Accessed 2019), MATLAB and GAMS: interfacing optimization and visualization software, University of Wisconsin. http://research.cs.wisc.edu/math-prog/matlab.html.
Meraklı, M. and Yaman, H., (2016). "Robust intermodal hub location under polyhedral demand uncertainty", Transportation Research Part B: Methodological, Vol. 86, pp. 66-85.
Momayezi, F., Chaharsooghi, S.K., Sepehri, M.M. and Kashan, A.H., (2018). "The capacitated modular single-allocation hub location problem with possibilities of hubs disruptions: modeling and a solution algorithm", Operational Research, pp.1-28.
Mou, D. and Chang, X., (2014). "An uncertain programming for the integrated planning of production and transportation", Mathematical Problems in Engineering.
Neamatian Monemi, R., Gelareh, S., Hanafi, S. and Maculan, N., (2017). "A co-opetitive framework for the hub location problems in transportation networks", Optimization, Vol. 66, No. 12, pp. 2089-2106.
Nechval, N., Purgailis, M., Rozevskis, U. and Nechval, K., (2013), July. Adaptive Stochastic Airline Seat Inventory Control under Parametric Uncertainty. In International Conference on Analytical and Stochastic Modeling Techniques and Applications (pp. 308-323). Springer, Berlin, Heidelberg.
O'kelly, M.E., (1987). "A quadratic integer program for the location of interacting hub facilities", European journal of operational research, Vol. 32, No. 3, pp. 393-404.
Setak, M., Feizizadeh, F., Tikani, H., & Ardakani, E. S. (2019). "A bi-level stochastic optimization model for reliable supply chain in competitive environments: Hybridizing exact method and genetic algorithm", Applied Mathematical Modelling, Vol. 75, pp. 310-332.
Sim, T., Lowe, T.J. and Thomas, B.W., (2009). "The stochastic p-hub center problem with service-level constraints", Computers & Operations Research, Vol. 36, No. 12, pp. 3166-3177.
Taherkhani, G. and Alumur, S.A., (2019). "Profit maximizing hub location problems", Omega, Vol. 86, pp. 1-15.
Tan, P.Z. and Kara, B.Y., (2007). "A hub covering model for cargo delivery systems", Networks: An International Journal, Vol. 49, No. 1, pp. 28-39.
Tikani, H., and Setak, M. (2019). "Efficient solution algorithms for a time-critical reliable transportation problem in multigraph networks with FIFO property", Applied Soft Computing, Vol. 74, pp. 504-528.
Tikani, H., Honarvar, M., and Mehrjerdi, Y. Z. (2016). "Joint optimization of star P-hub median problem and seat inventory control decisions considering a hybrid routing transportation system", International Journal of Supply and Operations Management, Vol. 3, No. 3, pp. 1.
Tikani, H., Honarvar, M., and Mehrjerdi, Y. Z. (2018). "Developing an integrated hub location and revenue management model considering multi-classes of customers in the airline industry", Computational and Applied Mathematics, Vol. 37, No. 3, pp. 3334-3364.
Topcuoglu, H., Corut, F., Ermis, M. and Yilmaz, G., (2005). "Solving the uncapacitated hub location problem using genetic algorithms", Computers & Operations Research, Vol. 32, No. 4, pp. 967-984.
Yang, T.H. and Chiu, T.Y., (2016). "Airline hub-and-spoke system design under stochastic demand and hub congestion", Journal of Industrial and Production Engineering, Vol. 33, No. 2, pp. 69-76.
Yang, T.H., (2009). "Stochastic air freight hub location and flight routes planning", Applied Mathematical Modelling, Vol. 33, No. 12, pp. 4424-4430.
Yoon, M.G., Lee, H.Y. and Song, Y.S., (2017). "Dynamic pricing & capacity assignment problem with cancellation and mark-up policies in airlines", Asia Pacific Management Review, Vol. 22, No. 2, pp. 97-103.
Zarandi, M.H.F., Davari, S. and Sisakht, A.H., (2011), June. Design of a reliable hub-and-spoke network using an interactive fuzzy goal programming. In 2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011) (pp. 2955-2959). IEEE.
Zhao, W. and Zheng, Y.S., (2001). "A dynamic model for airline seat allocation with passenger diversion and no-shows", Transportation Science, Vol. 35, No. 1, pp. 80-98.
)